The part about people with a visa for Canada, Japan, Schengen area, UK or US is just as the website says. It is not about passports. A person from a third country who holds one of above visas can enter Mexico without a Mexican visa.
Okay, so the correct information is: Most countries can travel to Mexico without a visa (for tourism for 180 days or less). Separately, nationals of other countries which would require a visa can travel to Mexico without a visa if they have a visa or non-citizenship permanent residence from the CA/JPN/EU/UK/US.
Thanks, I appreciate the clarification.